An institution isnt going to have trillions under management without big players.
What happens is like anything else: there is a haircut. So pension funds, as an example, will lose a percentage of their holdings. It is no different than the Russuan crisis in the late 1990s when a lot of money was lost on the bet there.
This will be more widespread.
So in that case, a possible scenario in the case of pension funds is a shortage of it when people need it.
That is always a major possibility and fall out from the mis-management of the financial industry.
Many pension funds in the developed world are vastly underfunded. It is going to be a major problem even if countries do not encounter a sovereign debt crisis.